What Is the Role of Frequency on Neural Activation in Tonic Stimulation in SCS Therapy? A Computational Study on Sensory Aβ Nerve Fibers

Abstract

The investigation of the effect of the stimulation parameters by computational modeling helps to understand the electrical response of specific neural elements in Spinal Cord Stimulation (SCS) therapy for chronic pain treatment. While the effect of the amplitude, the pulse width, and the electrode configuration on neural activation has been widely studied and is well-established in tonic stimulation, how frequency influences neural activation remains unclear. Thus, the aim of this work is to study the effect of frequency on the electrical response of sensory $\text{A}\beta $ neurons in tonic stimulation. Our approach consisted of the development of a new nerve fiber model from the combination of two previous models used in SCS modeling (the Wesselink-Holsheimer-Boom model and the Richardson-McIntyre-Grill model B). We simulate the action potential and the gates probabilities evolution of a $12.8~\mu \text{m}$ fiber diameter at different pulse frequencies (50, 350, 600, 800, and 1000 Hz). We also simulated the firing rate of two nerve fiber diameters (5.7 and $12.8~\mu \text{m}$ ) in function of pulse frequency (from 1 to 1400 Hz) at different pulse widths (100, 300, and $500~\mu \text{s}$ ). In the range of 2-1000 Hz, the firing rate of a $12.8~\mu \text{m}$ -diameter nerve fiber can be maximized by utilizing a 350 Hz, $300~\mu \text{s}$ -stimulus. Frequencies above 350 Hz reduce half to one-third the firing rate, and 1000 Hz-stimulus overrides the electrical activity of the sensory nerve fiber. Small fibers (5.7 $\mu \text{m}$ -diameter) present lower firing rate values than large fibers ( $12.8~\mu \text{m}$ -diameter). High values of pulse width decrease the firing rate of the nerve fibers as well as the range of frequencies that could be used to stimulate. According to the results, the frequency could have a considerable implication on the modulation of the firing rate of a nerve fiber. Thus, the frequency could play an important role to select and increase the activity of specific neural elements of the spinal cord in SCS therapy.